Modelling of membrane nanofiltration—pore size distribution effects

Abstract

The effects of log-normal pore size distributions on the rejection of uncharged solutes and NaCl at hypothetical nanofiltration membranes have been assessed theoretically. The importance of pore radius-dependent properties such as solvent viscosity and dielectric constant is increased by the introduction of a pore size distribution in calculations. However, the effect of porewise variation in viscosity is less apparent when considered at a defined applied pressure rather than at a defined flux, showing a further advantage of basing theoretical analysis of nanofiltration in terms of applied pressure. Truncated pore size distributions gave better agreement than full distributions with experimental rejection data for a Desal-DK nanofiltration membrane. Such truncation is in agreement with the findings of atomic force microscopy (AFM). Analysis of uncharged solute rejection data alone could not give useful information about membrane pore size distribution. Neither could such a distribution be obtained quantitatively directly from AFM images. However, use of the shape of the distribution obtained by AFM in conjunction with experimental rejection data for an uncharged solute allows calculation of corrected distributions. Importantly, incorporation of such a corrected pore size distribution in calculations of NaCl rejection gave better agreement with experimental data, compared to calculations assuming uniform pores, at high pressure, the region of industrial interest.